Find the direction cosines of the vector \(4i - 3j\).
Answer Details
Direction cosines are the cosines of the angles that a vector makes with the positive x, y and z axes.
Let's denote the vector by \(\mathbf{v} = 4\mathbf{i} - 3\mathbf{j} + 0\mathbf{k}\).
Then the direction cosines of \(\mathbf{v}\) are:
\begin{align*}
\cos\alpha &= \frac{4}{5} \\
\cos\beta &= \frac{-3}{5} \\
\cos\gamma &= 0
\end{align*}
Therefore, the correct option is:
- \(\frac{4}{5}, -\frac{3}{5}\)